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Worksheet: Velocity

In this worksheet, we will practice finding velocity as the rate of change of displacement, explaining the similarities and differences between speed and velocity.

Q1:

An object moves forward at 10 m/s
for 4 s and then moves
backward for 2 s at the same speed.
What net forward distance does the object move
from its starting position?

Q2:

An object moves left at a constant speed of
5 m/s
for 3 s. How
far does the object move to the left?

Q3:

An object moves north at 12 m/s
for 10 seconds and then
stops and stays
motionless for 10 seconds before
moving north at 12 m/s for
another 10 seconds.
What is the object’s average northward velocity?

Q4:

What is the average westward velocity of an object that
moves 11 m to the
west in a time of 0.25 s?

Q5:

A fish swims a distance of 15 m to the left at an average speed of 2 m/s
and then immediately turns around and swims half this distance to the right. The time that passes while all this occurs is 12 s, as shown in the diagram.
In this question, consider displacement to the left as positive.

What is the displacement of the fish from its starting point 12 s after it starts moving?

For how long does the fish swim to the left?

What is the fish’s average velocity while it moves to the right? Answer to one decimal place.

What is the average velocity of the fish over
the 12 s that the fish moves for?

Q6:

The change of an object’s displacement with time is shown in
the displacement–time graph. In which region of the graph is the speed of the
object decreasing?

AC to D

BA to B

CD to E

DB to C

EE to F

Q7:

What is the average eastward velocity of an object that moves
6 m east and
2 m west in a total time
of 0.75 s? Answer to one decimal place.

Q8:

A cyclist joins an east-west road and travels a distance of
240 m east at a speed of
12 m/s. He then
immediately turns around and travels a distance of 96 m
west at
the same speed that he traveled east at and then stops to dismount his bike.

What is the total time for which the cyclist moves?

What is the cyclist’s average velocity to the east from when he joins
the road to when he dismounts? Give
your answer to two decimal places.

Q9:

An object is initially at rest and then moves
100 m to the left and then
40 m to the right. The time taken
between the object first starting to move and having moved
40 m to the right is 20 seconds. What is the object’s average
velocity to the left for the 20 s after
it begins moving?

Q10:

The velocity-time graph shows the change in the velocity of a person walking in the time interval from
𝑡=0seconds to
𝑡=6seconds. The
person’s starting point is their position when 𝑡=0seconds.

What is the person’s displacement from their starting point after
2 seconds?

What is the person’s displacement from their starting point after 3 seconds?

What is the person’s displacement from their starting point after
4 seconds?

What is the person’s displacement from their starting point after
5 seconds?

Q11:

A drone flies along a triangular path that starts from and returns to a point 𝑃, as shown
in the diagram, initially heading north. The drone’s speed is a constant 1.5 m/s when
traveling north. The drone completes its eastward travel in the same time that it takes
it to complete its northward travel. On the last part of its travel, the drone moves diagonally at a constant speed that has the
average value of its northward speed in the first part of its travel and its eastward
speed in the second part of its travel.

What is the drone’s net displacement from the start of its motion to the end of its
motion?

How fast does the drone move eastward in the second part of its travel?

How fast does the drone move westward in the last part of its travel? Round your
answer to two decimal places.

How fast does the drone move southward in the last part of its travel? Round your
answer to two decimal places.

Q12:

A child kicks a ball and it moves along a horizontal ground toward a wall 2 m
away. The ball
moves at 2.25 m/s
toward the wall, hits the wall, and bounces half the distance straight back
to the child but moving only at an average speed of 1.75 m/s
after hitting the wall.

What total distance did the ball move?

What was the ball’s net displacement toward the wall?

How much time did the ball move for? Give your answer to two decimal places.

What was the ball’s average speed during its motion to the nearest meter per second?

What was the ball’s average velocity toward the wall from when the ball was kicked to when
it had rolled back from the wall and come to a stop? Give your answer to two decimal
places.

Q13:

A person is late for an appointment at an office that is at
the other end of a long straight road to their home. The person leaves
his home and runs toward his destination for a time of 45 seconds before
realizing that he has to return home to pick up some documents that he will
need at the appointment. The person runs back home at the same speed that he ran at before.
The person spends 185 seconds in their home finding the documents and then runs
toward their appointment again. This time, the person runs at 5.5 m/s
for 260 seconds and then arrives
at the office.

How much time passes between the person first leaving his house and arriving at his appointment?

What is the distance between the person’s house and their
office?

What is the person’s average velocity between first leaving his home and
finally arriving at the office? Give your answer to two decimal places.

Q14:

A child kicks a ball and it moves along a horizontal ground toward a wall
2 m away.
The ball moves at
2.25 m/s toward the wall,
hits the wall, and bounces half the distance straight back to the child,
moving only at an average speed of
1.75 m/s after hitting the wall.

What was the total distance the ball moved?

What was the ball’s net displacement toward the wall?

How much time did the ball move for? Give your answer to two decimal places.

What was the ball’s average speed during its motion, to the
nearest meter per second?

What was the ball’s average velocity toward the wall from when the ball was
kicked to when it rolled back from the wall and came to a stop? Give
your answer to two decimal places.